In a mixing bowl, combine all-purpose flour, icing sugar, cocoa powder, and a pinch of salt. Pour in the melted butter and add the vanilla extract, mixing well until a dough forms. Press this rich chocolate dough evenly into a tart pan, ensuring the sides are well-covered, then chill for 30 minutes to firm up.

Preheat your oven to 350°F (175°C). Once heated, prick the tart base with a fork to prevent bubbling, then bake for 15 minutes until set and slightly firm to the touch. Let the chocolate tart base cool completely on a wire rack.

In a medium saucepan, vigorously whisk together egg yolks, whole eggs, white sugar, cornstarch, and salt until combined. Gradually incorporate the whole milk and heavy cream, whisking continuously to create a smooth mixture. Heat over medium heat, stirring constantly until it thickens and begins to bubble, about 5–7 minutes. Remove from heat and stir in the chopped dark chocolate until fully melted and smooth.

Pour the velvety chocolate custard into the cooled tart shell, smoothing out the top with a spatula. Place the tart in the oven and reduce the temperature to 325°F (160°C). Bake for 45-50 minutes, until the custard is set but still slightly jiggly in the center.

After baking, allow the French chocolate flan to cool at room temperature for at least 1 hour. Once cooled, brush the top with jam for a beautiful glaze, then refrigerate until ready to serve.